Determination of high strain-rate constitutive material parameters from highly compliant, non-linear materials including hydrogels and soft tissues remains a significant challenge. To address this challenge we recently developed a laser-based Inertial Microcavitation Rheometry (IMR) technique, capable of constitutively characterizing soft materials at ultra-high strain-rates ($O\left(10^3\right)\sim O\left(10^8\right)s^{-1}$). This technique utilizes spatially-focused, and temporally-resolved, single cavitation bubbles in conjunction with a theoretical framework for determining the non-linear viscoelastic material properties of the surrounding soft material.

Here, by advancing our spatiotemporal imaging capability and tracking the motion of native material features close to the inertially cavitating bubble, we find significant deviation from the IMR predicted material displacements at a critical material Mach number of 0.08, marking the transition to violent collapse. Interestingly, this critical Mach number appears to be almost independent of the material properties of the surrounding hydrogel. We show that through proper temporal resolution of the cavitation dynamics, all of the highly nonlinear viscoelastic properties of the surrounding material can still be uniquely determined from just the first expansion and collapse cycle alone, as long as the local Mach number is below the critical threshold. Furthermore, we show that the inclusion of a higher order strain stiffening term on the rate-dependent non-linear spring can lead to better estimation of the material properties and full recovery of the equilibrium shear modulus, which was not possible with previous nonlinear neo-Hookean Kelvin–Voigt model formulations. Thus, the developments presented here significantly expand the applicability and robustness of IMR for accurately determining the rate-dependent, finite deformation constitutive behavior of soft materials.

从高度顺应的非线性材料（包括水凝胶和软组织）中确定高应变率本构材料参数仍然是一项重大挑战。为了应对这一挑战，我们最近开发了一种基于激光的惯性微空化流变仪（IMR）技术，该技术能够以超高应变率对软材料进行特征性表征（$Ø（\mathrm{1个}{0}^3）〜Ø（\mathrm{1个}{0}^8）s^{-\mathrm{1个}}$）。该技术利用空间聚焦和时间分辨的单个空化气泡，结合理论框架来确定周围软材料的非线性粘弹性材料特性。

在这里，通过提高我们的时空成像能力并跟踪接近惯性空化气泡的原始材料特征的运动，我们发现在关键材料马赫数为0.08时，与IMR预测的材料位移存在明显偏差，标志着向暴力塌陷的过渡。有趣的是，这个临界马赫数似乎几乎与周围水凝胶的材料特性无关。我们表明，通过适当的气蚀动力学的时间分辨率，只要局部马赫数低于临界阈值，仍然可以仅从第一个膨胀和坍塌循环就唯一地确定周围材料的所有高度非线性粘弹性。 。此外，我们表明，在取决于速率的非线性弹簧上包含更高阶的应变刚度项可以导致对材料性能的更好估计，以及平衡剪切模量的完全恢复，而以前的非线性新Hookean Kelvin则不可能–Voigt模型公式。因此，这里提出的发展显着扩展了IMR的适用性和鲁棒性，可以准确地确定速率依赖的，有限变形的软质材料的本构行为。